public static Vector128 <float> MaskExp(Vector128 <float> power, int exponentMask) { Vector128 <float> restrictedPower = Avx.Blend(power, AvxExtensions.BroadcastScalarToVector128(1.0F), (byte)exponentMask); Vector128 <float> exponent = Avx.Blend(MathV.Exp(restrictedPower), Vector128 <float> .Zero, (byte)exponentMask); return(exponent); }
public unsafe static Vector128 <float> Exp2(Vector128 <float> power) { Debug.Assert(Avx.MoveMask(Avx.And(Avx.CompareGreaterThan(power, AvxExtensions.BroadcastScalarToVector128(MathV.FloatMaximumPower)), Avx.CompareOrdered(power, power))) == 0); byte zeroMask = (byte)Avx.MoveMask(Avx.CompareLessThan(power, AvxExtensions.BroadcastScalarToVector128(-MathV.FloatMaximumPower))); Vector128 <float> integerPart = Avx.RoundToNearestInteger(power); Vector128 <float> integerExponent = Avx.ShiftLeftLogical(Avx.Add(Avx.ConvertToVector128Int32(integerPart), MathV.FloatMantissaZero128), MathV.FloatMantissaBits).AsSingle(); // evaluate polynomial Vector128 <float> beta1 = AvxExtensions.BroadcastScalarToVector128(MathV.Exp2Beta1); Vector128 <float> beta2 = AvxExtensions.BroadcastScalarToVector128(MathV.Exp2Beta2); Vector128 <float> beta3 = AvxExtensions.BroadcastScalarToVector128(MathV.Exp2Beta3); Vector128 <float> beta4 = AvxExtensions.BroadcastScalarToVector128(MathV.Exp2Beta4); Vector128 <float> x = Avx.Subtract(power, integerPart); // fractional part Vector128 <float> fractionalExponent = AvxExtensions.BroadcastScalarToVector128(MathV.One); fractionalExponent = Avx.Add(fractionalExponent, Avx.Multiply(beta1, x)); Vector128 <float> x2 = Avx.Multiply(x, x); fractionalExponent = Avx.Add(fractionalExponent, Avx.Multiply(beta2, x2)); Vector128 <float> x3 = Avx.Multiply(x2, x); fractionalExponent = Avx.Add(fractionalExponent, Avx.Multiply(beta3, x3)); Vector128 <float> x4 = Avx.Multiply(x3, x); fractionalExponent = Avx.Add(fractionalExponent, Avx.Multiply(beta4, x4)); // form exponent Vector128 <float> exponent = Avx.Multiply(integerExponent, fractionalExponent); // suppress exponent overflows by truncating values less than 2^-127 to zero if (zeroMask != 0) { exponent = Avx.Blend(exponent, Vector128 <float> .Zero, zeroMask); } return(exponent); }
public unsafe static Vector128 <float> Log2(Vector128 <float> value) { // split value into exponent and mantissa parts Vector128 <float> one = AvxExtensions.BroadcastScalarToVector128(MathV.One); Vector128 <int> integerValue = value.AsInt32(); Vector128 <float> exponent = Avx.ConvertToVector128Single(Avx.Subtract(Avx.ShiftRightLogical(Avx.And(integerValue, MathV.FloatExponentMask128), MathV.FloatMantissaBits), MathV.FloatMantissaZero128)); Vector128 <float> mantissa = Avx.Or(Avx.And(integerValue, MathV.FloatMantissaMask128).AsSingle(), one); // evaluate mantissa polynomial Vector128 <float> beta1 = AvxExtensions.BroadcastScalarToVector128(MathV.Log2Beta1); Vector128 <float> beta2 = AvxExtensions.BroadcastScalarToVector128(MathV.Log2Beta2); Vector128 <float> beta3 = AvxExtensions.BroadcastScalarToVector128(MathV.Log2Beta3); Vector128 <float> beta4 = AvxExtensions.BroadcastScalarToVector128(MathV.Log2Beta4); Vector128 <float> beta5 = AvxExtensions.BroadcastScalarToVector128(MathV.Log2Beta5); Vector128 <float> x = Avx.Subtract(mantissa, one); Vector128 <float> polynomial = Avx.Multiply(beta1, x); Vector128 <float> x2 = Avx.Multiply(x, x); polynomial = Avx.Add(polynomial, Avx.Multiply(beta2, x2)); Vector128 <float> x3 = Avx.Multiply(x2, x); polynomial = Avx.Add(polynomial, Avx.Multiply(beta3, x3)); Vector128 <float> x4 = Avx.Multiply(x3, x); polynomial = Avx.Add(polynomial, Avx.Multiply(beta4, x4)); Vector128 <float> x5 = Avx.Multiply(x4, x); polynomial = Avx.Add(polynomial, Avx.Multiply(beta5, x5)); // form logarithm return(Avx.Add(exponent, polynomial)); }
public unsafe static Vector128 <float> Exp(Vector128 <float> power) { return(MathV.Exp2(Avx.Multiply(AvxExtensions.BroadcastScalarToVector128(MathV.ExpToExp2), power))); }
public unsafe static Vector128 <float> Log10(Vector128 <float> value) { return(Avx.Multiply(AvxExtensions.BroadcastScalarToVector128(MathV.Log2ToLog10), MathV.Log2(value))); }
public static unsafe float GetScribnerBoardFeetPerAcre(Trees trees) { // for now, assume all trees are of the same species if (trees.Species != FiaCode.PseudotsugaMenziesii) { throw new NotSupportedException(); } if (trees.Units != Units.English) { throw new NotSupportedException(); } // Douglas-fir #if DEBUG Vector128 <float> v6p8 = AvxExtensions.BroadcastScalarToVector128(6.8F); Vector128 <float> v10k = AvxExtensions.BroadcastScalarToVector128(10.0F * 1000.0F); #endif // constants Vector128 <float> forestersEnglish = AvxExtensions.BroadcastScalarToVector128(Constant.ForestersEnglish); Vector128 <float> one = AvxExtensions.BroadcastScalarToVector128(1.0F); Vector128 <float> six = AvxExtensions.BroadcastScalarToVector128(6.0F); Vector128 <float> vm3p21809 = AvxExtensions.BroadcastScalarToVector128(-3.21809F); // b4 Vector128 <float> v0p04948 = AvxExtensions.BroadcastScalarToVector128(0.04948F); Vector128 <float> vm0p15664 = AvxExtensions.BroadcastScalarToVector128(-0.15664F); Vector128 <float> v2p02132 = AvxExtensions.BroadcastScalarToVector128(2.02132F); Vector128 <float> v1p63408 = AvxExtensions.BroadcastScalarToVector128(1.63408F); Vector128 <float> vm0p16184 = AvxExtensions.BroadcastScalarToVector128(-0.16184F); Vector128 <float> v1p033 = AvxExtensions.BroadcastScalarToVector128(1.033F); Vector128 <float> v1p382937 = AvxExtensions.BroadcastScalarToVector128(1.382937F); Vector128 <float> vm0p4015292 = AvxExtensions.BroadcastScalarToVector128(-0.4015292F); Vector128 <float> v0p087266 = AvxExtensions.BroadcastScalarToVector128(0.087266F); Vector128 <float> vm0p174533 = AvxExtensions.BroadcastScalarToVector128(-0.174533F); Vector128 <float> vm0p6896598794 = AvxExtensions.BroadcastScalarToVector128(-0.6896598794F); // rc6-rs632 Vector128 <float> v0p993 = AvxExtensions.BroadcastScalarToVector128(0.993F); Vector128 <float> v0p174439 = AvxExtensions.BroadcastScalarToVector128(0.174439F); Vector128 <float> v0p117594 = AvxExtensions.BroadcastScalarToVector128(0.117594F); Vector128 <float> vm8p210585 = AvxExtensions.BroadcastScalarToVector128(-8.210585F); Vector128 <float> v0p236693 = AvxExtensions.BroadcastScalarToVector128(0.236693F); Vector128 <float> v0p00001345 = AvxExtensions.BroadcastScalarToVector128(0.00001345F); Vector128 <float> v0p00001937 = AvxExtensions.BroadcastScalarToVector128(0.00001937F); Vector128 <float> v1p001491 = AvxExtensions.BroadcastScalarToVector128(1.001491F); Vector128 <float> vm6p924097 = AvxExtensions.BroadcastScalarToVector128(-6.924097F); Vector128 <float> v0p912733 = AvxExtensions.BroadcastScalarToVector128(0.912733F); Vector128 <float> v0p00001351 = AvxExtensions.BroadcastScalarToVector128(0.00001351F); fixed(float *dbh = &trees.Dbh[0], expansionFactors = &trees.LiveExpansionFactor[0], height = &trees.Height[0]) { Vector128 <float> standBoardFeetPerAcre = Vector128 <float> .Zero; for (int treeIndex = 0; treeIndex < trees.Count; treeIndex += Constant.Simd128x4.Width) { Vector128 <float> dbhInInches = Avx.LoadVector128(dbh + treeIndex); Vector128 <float> heightInFeet = Avx.LoadVector128(height + treeIndex); Vector128 <float> logDbhInInches = MathV.Log10(dbhInInches); Vector128 <float> logHeightInFeet = MathV.Log10(heightInFeet); // FiaCode.PseudotsugaMenziesii => -3.21809F + 0.04948F * logHeightInFeet * logDbhInInches - 0.15664F * logDbhInInches * logDbhInInches + // 2.02132F * logDbhInInches + 1.63408F * logHeightInFeet - 0.16184F * logHeightInFeet * logHeightInFeet, Vector128 <float> cvtsl = Avx.Add(vm3p21809, Avx.Multiply(v0p04948, Avx.Multiply(logHeightInFeet, logDbhInInches))); cvtsl = Avx.Add(cvtsl, Avx.Multiply(vm0p15664, Avx.Multiply(logDbhInInches, logDbhInInches))); cvtsl = Avx.Add(cvtsl, Avx.Multiply(v2p02132, logDbhInInches)); cvtsl = Avx.Add(cvtsl, Avx.Multiply(v1p63408, logHeightInFeet)); cvtsl = Avx.Add(cvtsl, Avx.Multiply(vm0p16184, Avx.Multiply(logHeightInFeet, logHeightInFeet))); Vector128 <float> cubicFeet = MathV.Exp10(cvtsl); Vector128 <float> dbhSquared = Avx.Multiply(dbhInInches, dbhInInches); // could be consolidated by merging other scaling constants with Forester's constant for basal area Vector128 <float> basalAreaInSquareFeet = Avx.Multiply(forestersEnglish, dbhSquared); // b4 = cubicFeet / (1.033F * (1.0F + 1.382937F * MathV.Exp(-4.015292F * dbhInInches / 10.0F)) * (basalAreaInSquareFeet + 0.087266F) - 0.174533F); Vector128 <float> b4 = Avx.Divide(cubicFeet, Avx.Add(Avx.Multiply(v1p033, Avx.Multiply(Avx.Add(one, Avx.Multiply(v1p382937, MathV.Exp(Avx.Multiply(vm0p4015292, dbhInInches)))), Avx.Add(basalAreaInSquareFeet, v0p087266))), vm0p174533)); Vector128 <float> cv4 = Avx.Multiply(b4, Avx.Subtract(basalAreaInSquareFeet, v0p087266)); // conversion to Scribner volumes for 32 foot trees // Waddell 2014:32 // rc6 = 0.993F * (1.0F - MathF.Pow(0.62F, dbhInInches - 6.0F)); Vector128 <float> rc6 = Avx.Multiply(v0p993, Avx.Subtract(one, MathV.Exp(Avx.Multiply(vm0p6896598794, Avx.Subtract(dbhInInches, six))))); // log2(0.62) = -0.6896598794 Vector128 <float> cv6 = Avx.Multiply(rc6, cv4); Vector128 <float> logB4 = MathV.Log10(b4); // float rs616 = MathF.Pow(10.0F, 0.174439F + 0.117594F * logDbhInInches * logB4 - 8.210585F / (dbhInInches * dbhInInches) + 0.236693F * logB4 - 0.00001345F * b4 * b4 - 0.00001937F * dbhInInches * dbhInInches); Vector128 <float> rs616l = Avx.Add(v0p174439, Avx.Multiply(v0p117594, Avx.Multiply(logDbhInInches, logB4))); rs616l = Avx.Add(rs616l, Avx.Divide(vm8p210585, dbhSquared)); rs616l = Avx.Add(rs616l, Avx.Multiply(v0p236693, logB4)); rs616l = Avx.Subtract(rs616l, Avx.Multiply(v0p00001345, Avx.Multiply(b4, b4))); rs616l = Avx.Subtract(rs616l, Avx.Multiply(v0p00001937, dbhSquared)); Vector128 <float> rs616 = MathV.Exp10(rs616l); Vector128 <float> sv616 = Avx.Multiply(rs616, cv6); // Scribner board foot volume to a 6 inch top for 16 foot logs // float rs632 = 1.001491F - 6.924097F / tarif + 0.00001351F * dbhInInches * dbhInInches; Vector128 <float> rs632 = Avx.Add(v1p001491, Avx.Divide(vm6p924097, Avx.Multiply(v0p912733, b4))); rs632 = Avx.Add(rs632, Avx.Multiply(v0p00001351, dbhSquared)); Vector128 <float> zeroVolumeMask = Avx.CompareLessThanOrEqual(dbhInInches, six); Vector128 <float> sv632 = Avx.Multiply(rs632, sv616); // Scribner board foot volume to a 6 inch top for 32 foot logs sv632 = Avx.BlendVariable(sv632, Vector128 <float> .Zero, zeroVolumeMask); #if DEBUG DebugV.Assert(Avx.CompareGreaterThanOrEqual(Avx.BlendVariable(rc6, Vector128 <float> .Zero, zeroVolumeMask), Vector128 <float> .Zero)); DebugV.Assert(Avx.CompareLessThanOrEqual(rc6, one)); DebugV.Assert(Avx.CompareGreaterThanOrEqual(Avx.BlendVariable(rs616, one, zeroVolumeMask), one)); DebugV.Assert(Avx.CompareLessThanOrEqual(Avx.BlendVariable(rs616, Vector128 <float> .Zero, zeroVolumeMask), v6p8)); DebugV.Assert(Avx.CompareGreaterThanOrEqual(Avx.BlendVariable(rs632, Vector128 <float> .Zero, zeroVolumeMask), Vector128 <float> .Zero)); DebugV.Assert(Avx.CompareLessThanOrEqual(Avx.BlendVariable(rs632, Vector128 <float> .Zero, zeroVolumeMask), one)); DebugV.Assert(Avx.CompareGreaterThanOrEqual(Avx.BlendVariable(sv632, Vector128 <float> .Zero, zeroVolumeMask), Vector128 <float> .Zero)); DebugV.Assert(Avx.CompareLessThanOrEqual(Avx.BlendVariable(sv632, Vector128 <float> .Zero, zeroVolumeMask), v10k)); #endif Vector128 <float> expansionFactor = Avx.LoadVector128(expansionFactors + treeIndex); standBoardFeetPerAcre = Avx.Add(standBoardFeetPerAcre, Avx.Multiply(expansionFactor, sv632)); } standBoardFeetPerAcre = Avx.HorizontalAdd(standBoardFeetPerAcre, standBoardFeetPerAcre); standBoardFeetPerAcre = Avx.HorizontalAdd(standBoardFeetPerAcre, standBoardFeetPerAcre); return(standBoardFeetPerAcre.ToScalar()); } }